Hallelujah. Heathrow's third runway is history, the biggest victory for the environment movement since the scrapping of the last Tory government's road-building programme. Gone, too, is the planned expansion of Gatwick and Stansted (though the government has so far said nothing about airport expansion elsewhere). Instead we'll have a high-speed railway connecting London to Birmingham, Manchester and Leeds. All hail to the new age of the train. Perhaps.

I don't dispute the problem. Both roads and railways are close to gridlock. New motorways, government figures show, scarcely improve journey times between city centres. Upgrading old railways snarls up the system even more, costs a fortune and adds little to their capacity.

New lines, by contrast, free up the old tracks for freight and local trains. They allow companies to run longer trains and additional services. High-speed rail cuts journey times almost twice as much as new conventional tracks while costing scarcely any more. The greenhouse gases it produces will be cancelled out by people switching from planes to trains. What's not to like?

What's not to like is that the case has not been made. The background data on which these claims are based isn't just sparse – in some cases it's non-existent. Where it does exist, it starkly contradicts other government figures. I wanted to be convinced, perhaps I still could be. But the Department for Transport's argument currently consists of several thousand pages of wishful thinking.

The last government's command paper contains a graph showing carbon figures for air, road, conventional rail and high-speed trains. This creates the impression that high-speed rail produces less than half as much carbon per passenger kilometre as conventional railways, and just a fraction of the emissions from cars. How did it produce these results? By selecting Eurostar – and apparently only the French section – as its example of a high-speed train. French electricity is mostly produced by nuclear power, so high-speed trains there create much smaller emissions than ours would cause. It also appears to have ignored the carbon costs of construction.

Compare this to a paper commissioned by the Department for Transport in 2007. When construction is taken into account, high-speed rail journeys from London to Manchester will produce 60% more carbon than conventional rail and 35% more carbon than car journeys. They will generate only 25% less carbon than plane travel (all references are on my website).

Throughout the recent government documents there's an assumption that the new railway will be sustainable because it will draw people out of planes. But buried on page 162 of the report on which the department has based its case, published in March 2010, are the figures that derail this assumption. Of the passengers expected to use the new railway, 57% would otherwise have travelled by conventional train, 27% wouldn't have travelled at all, 8% would have gone by car and 8% by air. In other words, 92% of its customers are expected to switch to high-speed rail from less polluting alternatives. Yet the same report contains a table (page 179) suggesting that the savings from flights not taken outweigh the entire carbon costs of the railway. It provides neither source nor justification.

The 2007 report shows that even if everyone flying between London and Manchester switched to the train, the savings wouldn't compensate for the extra emissions a new line would cause. "There is no potential carbon benefit in building a new line on the London to Manchester route over the 60-year appraisal period." A switch from plane to train could even increase emissions. Unless the landing slots at present used by domestic flights are withdrawn by the government, they are likely to be used instead for international flights. The government has no plan for reducing total airport space.

The business case the department has produced is just as shaky. The first thing that jumps out at you is that the government has conflated it with the cost-benefit analysis. They are not the same thing. The business case is as follows: the government shells out £25.5bn, loses a net £1.5bn in tax and gets £15bn back over 60 years from fares. Net loss to the government: £12bn. The cost-benefit analysis (which the government calls "the business case") produces benefits of £32.3bn. The department concludes that the scheme has a benefit-cost ratio of 2.7. But where did the £32.3bn come from?

Almost all of it is money deemed to have been saved by reducing travel times. Business customers, it says, will save £17.6bn by getting there faster; leisure customers £11.1bn. Nowhere in the documents are these figures explained or justified. I spent the whole of Monday pressing the Department for Transport, asking for an explanation of how it converted time into money. The department spent eight hours of frantic searching to discover, just before 5pm, that it did indeed have a model, which it described as "frightfully complicated".

By then my copy deadline was almost up, so I cannot tell you whether or not its consultants accounted for the fact that business travellers can work on the train, sometimes as productively as they can in the office. Nor can I say how it priced leisure travel. Are we to assume that an extra 20 minutes spent watching the telly when you get to your hotel is a benefit to which a price can be attached? How much is an hour with your granny worth? Whatever the answers may be, none of it translates into government revenue: assumed and equivocal benefits are being weighed against real spending.

Underlying these questions is a much bigger one: what's it all for? The department argues that high-speed rail is necessary because economic growth encourages people to travel more. High-speed rail, it says, will stimulate growth. This will encourage people to travel more, which will … For how much longer can this go on? At what point do we decide that this crowded little island is busy enough?

The answer from old and new governments appears to be never. The Department for Transport expects flying to increase by 178% between 2008 and 2033, driving by 43% and train journeys by 150%. It does not seek to cut this demand, only to accommodate it, until England becomes a giant transport corridor. Progress is measured by the number of people in transit. Civilisation will have reached its apogee when the entire population of Manchester takes the train every day to London and the entire population of London takes the train every day to Manchester. Perhaps we should resolve Britain's railway network into a single orbital system, so we can all remain in constant circulation. Then we'll know we're getting somewhere.

Yes, it's better to take a high-speed train than to fly. It would be better still not to have to make the journey at all, and to have some peace and stillness in our lives. And it would be better to have an honest, informed discussion about high-speed rail, rather than a wild guess based on unfounded assumptions and dodgy figures.

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